Solve for $x$, ignoring any extraneous solutions: $\dfrac{x^2 + 2x}{x + 6} = \dfrac{-2x + 12}{x + 6}$
Solution: Multiply both sides by $x + 6$ $ \dfrac{x^2 + 2x}{x + 6} (x + 6) = \dfrac{-2x + 12}{x + 6} (x + 6)$ $ x^2 + 2x = -2x + 12$ Subtract $-2x + 12$ from both sides: $ x^2 + 2x - (-2x + 12) = -2x + 12 - (-2x + 12)$ $ x^2 + 2x + 2x - 12 = 0$ $ x^2 + 4x - 12 = 0$ Factor the expression: $ (x - 2)(x + 6) = 0$ Therefore $x = 2$ or $x = -6$ However, the original expression is undefined when $x = -6$. Therefore, the only solution is $x = 2$.